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Question Number 132439 by liberty last updated on 14/Feb/21

$$$$$$\mathrm{it}\mathrm{is}\mathrm{a}\mathrm{known}\mathrm{that}\mathrm{a}\mathrm{particular}$$$$\mathrm{machine}\mathrm{will}\mathrm{make}\mathrm{product}\mathrm{with}$$$$\mathrm{a}\mathrm{qualified}\mathrm{rate}\mathrm{of}90\mathrm{\%}\mathrm{when}\mathrm{it}\mathrm{is}$$$$\mathrm{running}\mathrm{well},\mathrm{but}\mathrm{will}\mathrm{do}\mathrm{so}\mathrm{with}$$$$\mathrm{a}\mathrm{qualified}\mathrm{rate}\mathrm{of}\mathrm{only}30\mathrm{\%}\mathrm{when}$$$$\mathrm{it}\mathrm{is}\mathrm{not}\mathrm{running}\mathrm{well}.\mathrm{The}$$$$\mathrm{probability}\mathrm{that}\mathrm{machine}\mathrm{is}$$$$\mathrm{running}\mathrm{well}\mathrm{is}75\mathrm{\%}\mathrm{normally}.$$$$\mathrm{Suppose}\mathrm{that}\mathrm{one}\mathrm{day}\mathrm{the}\mathrm{first}$$$$\mathrm{product}\mathrm{made}\mathrm{by}\mathrm{the}\mathrm{machine}\mathrm{is}$$$$\mathrm{qualified}.\mathrm{Find}\mathrm{the}\mathrm{probabiliy}$$$$\mathrm{that}\mathrm{the}\mathrm{machine}\mathrm{is}\mathrm{running}\mathrm{well}\mathrm{at}$$$$\mathrm{this}\mathrm{time}.$$

Commented by bemath last updated on 14/Feb/21

$$\mathrm{p}=0.9$$

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